Four dimensional network



Dec. 24, 1957 w. H. NEwELL 2,817,478

FOUR DIMENSIONAL NETWORK Filed Nov. 22,-1952 AAAAA fm1/M, YN)

IN I/EN TOR.

H y A12a, 25 M//u/Af//Nfwfu gyzz/MW TTORNEI FOUR DIMENSIONAL NETWDRK William H. Newell, Mount Vernon, N. Y., assgnor to Sperry Rand Corporation, a corporation of Delaware Application November 22, 1952, Serial No. 322,000

2 Claims. (Cl. 23S-61) This invention relates to an electrical computing system for the solution of equations involving four variables.

One object of the invention is the determination of the value of X, where X=f(H, V, Y), when the values of H, V and Y and their functional relationships are known.

It is generally known that a potentiometer system can be used in a circuit to synthesize non-linear as well as linear continuous functions. Rheostat windings may vary in impedance per unit length in accordance with any given function. The potentiometers or voltage dividers used in the present invention have coils which are wound to synthesize functions of three variables. According to the invention there has been pre-set into each voltage divider in the system the independent term for the first variable and two fixed values for the second and third variables the desired output being tapped by sliding an adjustable contact slider to the proper calibrated point on the rheostat winding in accordance with the known input for the independent term. The voltage that is tapped from each voltage divider is, therefore, a function of two pre-selected fixed values for the second and third independent terms in the equation and an interpolated output for the first independent term. The tapped xed values are not necessarily the true ones desired as inputs for the first and second independent terms. These terms are represented on common potentiometers, and the voltage dividers are so arranged that one or the other of the pre-selected fixed quantities for the independent terms are in successive incremental relation. The increments are introduced into the common potentiometers from the voltage dividers and sliders in adjustable contact with the common potentiometers are employed for interpolation. The true inputs for the terms represented on the common potentiometers are thereby introduced.

The potentiometer system, which is hereinafter described in detail is an arrangement of potentiometers or voltage dividers in rows and columns. Their coils represent one independent term and two fixed quantities for the second and third terms. The arrangement in the rows is such that the coils will yield ordered increments for one of the independent terms and the same value for the other while the yield in the columns with respect to these quantities is the reverse. There is a common potentiometer provided for each row which is connected by adjustable sliders to the individual potentiometers. These common potentiometers are themselves connected to a single common potentiometer by adjustable sliders. The common potentiometers are provided with windings which synthesize one of the other variable terms. The preselected increments are introduced into the common potentiometers as inputs for the variable terms synthesized thereon. Where these inputs are not the desired ones, the adjustable sliders for the common potentiometers can be employed for tapping a voltage intermediate to those voltages which result from the most nearly correct pre-selected inputs.

The system can be greatly simplified if the output to be rates Patent C computed varies linearly, or nearly so, with one of the inputs because the successive increments between the rows or columns can be larger and for selected limits fewer potentiometers need be employed. Also, of course, the allowable magnitude of error controls the size of the system.

lt is understood that the invented system may be employed to solve functions having more than four variables without departing in substance or principle from the enclosed invention which is more fully described in the specification and illustrated by the accompanying drawings.

Fig. 1 is a diagrammatic view of the circuit arrangement for the invention.

Fig. 2 demonstrates graphically the functional relationship between the function, represented by X and one of the three independent variables at Various fixed values for the other variables.

The potentiometer system for solving equations hav ing three independent variables, as envisaged by the invention, embraces a plurality of potentiometers arranged in a plurality of rows. The number of rows .and the number in each row depend largely on the magnitudes of the maximum and minimum values in the corresponding terms in the equation to be solved and the linearity of the variable functions for these terms. In general the greater the linearity, the larger are the permissible input increments for the variables. The entire system is connected across a common alternating current source. The potentiometers in each row are in parallel.

The individual potentiometers are wound to represent one independent variable term and two predetermined fixed values for the other variable terms in the function. The potentiometers in row A, for example, are all wound to synthesize the variable term H which is one of the three independent variables of the function f (H, V, Y) to be solved. A constant or fixed value Y1 is also represented on each potentiometer, in row A. The potentiometers in this row differ only in respect to a fixed input value for the V variable term in the function in that successive increments V1 VM-l, VM are represented on successive windings. Any one of these predetermined values for V may be introduced by sliders H into row A common potentiometer PA the winding of which synthesizes the variable term for V in the equation. The row A common potentiometer will yield a value of the function for the desired H input, a fixed input for the variable Y and properly interpolated input quantity for the second variable V. A slider V in adjustable contact with common potentiometer PA accordingly taps off the correct output term values for H and V in the function and a fixed input value for the third variable Y. its function and operation is the same in all the rows.

The windings on the potentiometers of the remaining rows, as shown in Fig. l, B and N, are identical for each column 1l, 21, N1; 12, 22, N2; 1M-1, 2M-1, NM-l; 1M, 2M, NM, except for the increments of a preselected input value for the variable Y. Thel V sliders are moved to the same corresponding position on the common potentiometers PB PN for each row `and are connected to a common potentiometer PX for the columns. The function of the variable Y is synthesized by its winding. Slider Y in adjustable contact with common potentiometer PX is provided to interpolate the increments of Y in the same manner as sliders V are employed to interpolate the increments of V on the common potentiometers PA PN for the rows. A solution is accordingly given for the function `of H, V and Y with the desired input values substituted in the variable terms.

In Fig. 2, X is plotted against H at various values for V and Y1. The group of curves in (n) illustrates aeimvs 3 the functional relationship of X and H as established by the individual windings of the potentiometers in the A row. As shown in Fig. 1, the interpolation for V is made between V1 and V2. The dotted curve in (a) of Fig. 2 also illustrates the functional relationship between X and H for the proper input for one 'of the other variables V and a xed value for another variable Y. Similarly the curves in (b) of Fig. 2 illustrate the functional :relationship of X and H at the assigned increments of Y at the desired input for V. As seen in Fig. 1 interpolation on the common potentiometer PX is made between the A and B rows. Since Y1 and Y2 are the assigned values for Y in these rows the interpolated XH curve for Y1 shown as dotted in (b) is intermediate the Y1 and Y2 curves.

lparticular embodiment described which is set forth for i-llustrative purposes only and is not intended to be limited thereto.

What is claimed is:

1. A computer for solving an equation having three independent variables comprising a potentiometer system which includes a source of current, a plurality of indi- Avidual potentiometers arranged in rows and columns,

each potentiometer in the computer being in parallel across said source of current, successive potentiometers in the rows having windings representing the first independent variable, successive xed increments for the second variable and a Iixed value for the third variable, successive potentiorneters in the columns having, windings representing the first of said independent variables, iixed values for said second variable and successive fixed increments for said third variable, sliders in adjustable Contact with each potentiometer winding for tapping the desired output value for said first independent variable and iixed values for said second and third variables, common potentiometers for each row in connection with said sliders being powered exclusively thereby and wound to represent said second variable, a slider in adjustable contact with each of said common potentiometers for interpola tion of the increments of the said second variable thus yielding the desired outputs for the rst and second variables and xed increments for the third variable, a common potentiometer for the -columns in connection with said last ymentioned sliders being wound to represent said third independent variable, and a slider in adjustable contact with said second common potentiometer for interpolation of the fixed increments for the third variable thus yielding a solution of a function having three independent variables.

2. A computer for "generating a function having three independent variables comprising a potentiometer ,system which includes Ia source of current, .a plurality of individual potentiometers arranged in rows and columns, each potentiometer :in the `'computer being in parallel across said source of current, successive potentiometers in the rows having windings representing the first independent variable, successive iixed increments for the second variable and a fixed value for the third variable, successive potentiometers in the columns having windings representing the first of said independent variables, a xed value for said second variable and successive fixed increments for said third variable, each of sai-d rows of potentiometers having a separately driven common potentiometer, each of said common potentiometers for each row being in tapped connection with the several potentiometers in each row, and an additional common potentiometer for the colum-ns in tapped connection with each of said comm-on potentiometers for the rows whereby said additional common potentiometer is adapted to yield the dependent value of the function for which the values of its independent variables are known.

References Cited in the le of this patent UNITED STATES PATENTS 1,893,009 Ward Jan. 3, 1933 2,417,093 WllCOX Mar. 1l, 1947 2,468,150 .Wilcox Apr. 26, 1949 2,469,628 Bowman et al. May 10, 1949 2,500,997 Morgan Mar. 2l, 1.9.50 2,603,345 Walker Aug. 26, 1952 CTHER REFERENCES ElectronicAnalog lComputers (Korn and Korn), published .by McGraw-Hill Book Company, Inc., New York, 1952; copy received by the Patent Oice Library July 21, 1952. 

